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A geometric description of the extreme Khovanov cohomology

Part of: Low-dimensional topology

Published online by Cambridge University Press:  28 December 2017

J. González-Meneses ,
P. M. G. Manchón  and
M. Silvero
J. González-Meneses
Affiliation:
Departamento de Álgebra, Facultad de Matemáticas, Instituto de Matemáticas (IMUS), Universidad de Sevilla, Apdo. 1160, 41080 Sevilla, Spain (meneses@us.es)
P. M. G. Manchón
Affiliation:
Departamento de MatemÁtica Aplicada, ETSIDI-Universidad Politécnica de Madrid, Ronda de Valencia 3, 28012 Madrid, Spain (pedro.gmanchon@upm.es)
M. Silvero
Affiliation:
Departamento de Álgebra, Facultad de MatemÁticas, Instituto de MatemÁticas (IMUS), Universidad de Sevilla, Apdo. 1160, 41080 Sevilla, Spain (marithania@us.es)
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Abstract

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We prove that the potential extreme Khovanov cohomology of a link is the cohomology of the independence simplicial complex of its Lando graph. We also provide a family of knots having as many non-trivial extreme Khovanov cohomology modules as desired, that is, examples of H-thick knots that are as far from being H-thin as desired.

Keywords

knots and linksKhovanov cohomologyindependence complexH-thick knotsLando graph

MSC classification

Secondary: 57M27: Invariants of knots and 3-manifolds 57M25: Knots and links in $S^3$ 57M15: Relations with graph theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 3 , June 2018 , pp. 541 - 557
Copyright
Copyright © Royal Society of Edinburgh 2018